In this article we focus our attention on projection-based reduced order models
specifically tailored to geometrically parametrized problems [1]}, [2]}. The
idea is to combine the recently proposed Shifted Boundary Method
[3]}, [4]}, [5]} with Reduced Order Models based on the Proper Orthogonal Decomposition (POD) with Galerkin projection (SBM-ROM). This
combination, that has been recently proposed in previous works in a different
setting
[6]}, [7]}, [8]},
allows to avoid the map of all the parametrized solutions to a common reference
geometry, see also [9]}, [10]}.
In this paper, the embedded methodology introduced in the
mentioned research works is extended to shallow water equations with explicit
time marching schemes.
The idea of merging embedded approaches with reduced order models has been
proposed also in [11]} where a fictitious domain method was
coupled with a Proper Generalized Decomposition approach to study uncertain
geometries. In [12]} the authors proposed a projection based reduced
order model starting from an embedded full order simulation applied to evolving
interfaces.
